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Find the equation of the line with slope 1 that is tangent to the curve y=1/x1 
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#1
Feb2012, 03:45 PM

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1. The problem statement, all variables and given/known data
Find the equation of the line with slope 1 that is tangent to the curve y=1/x1 2. Relevant equations y=1/x1 3. The attempt at a solution Slope of 1 means y=1x+k So... 1x+k = 1/x1 I don't know how to rearrange this into a quadratic equation so that I can solve this. I know I use b^24ac=0 and substituting for a, b and c.... I'm just stuck on rearranging the equation into the form: ax^2+bx+c=0 


#2
Feb2012, 04:17 PM

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I'm going to guess that you are in a class that has discussed how to find the tangent to a curve. 


#3
Feb2012, 04:26 PM

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OTOH, maybe this actually is a precalculustype problem. What does it mean to say that a line is tangent to a curve?
For your equation, x + k = 1/x  1, what about multiplying both sides by x? 


#4
Feb2012, 04:34 PM

P: 9

Find the equation of the line with slope 1 that is tangent to the curve y=1/x1
(1/x1)(x) = ? You're right, but I'm confused as to how to multiply the second part? x/x^2x ? 


#5
Feb2012, 04:45 PM

P: 9

Here's my second stab at it...
1x+k = 1/x1 Rearranged: x^2+kx1 Using the discriminant of the quadratic formula: (b^24ac) a=1 b=k^2 c=1 k^24(1)(1)=0 Solving: k = 2 Therefore the equation is y=1x2 For the line with a slope of 1 that is tangent to the curve of 1/x1 Can anybody verify if I got this right? 


#6
Feb2012, 04:49 PM

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#7
Feb2012, 04:50 PM

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What is x * (1)? 


#8
Feb2012, 04:52 PM

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From post #3:



#9
Feb2012, 08:33 PM

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RGV 


#10
Feb2012, 08:39 PM

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